An experiment??

[Qoeleth]

You have no idea what you are talking about, do you? A probability is defined as existing between 0 and 1 (0% and 100%), so it is not possible to have a probability over 1 (100%). It is stuff and nonsense to state it is possible.

Further, if you are asking for the probability of writing one page out of 10[sup]500[/sup], then the probability is not infinite but infinitesimal as the probability is defined as P = particular option / total options. Thus, you would have a probability of writing that particular page as 10[sup]-500[/sup]!!!

So no, it must not have happened already.

I realise traditionally proability is between 0 and 1, expressed as a fraction of the outcome in question over the possible outcomes.

But, what if the number of possibilities of the outcome in question is infinite (e.g. there are an infinite number of possible true statements- since a truth could be stated about every possible aspect of, say, God), but the number of possible outcomes is limited (owing the the finite combinations of letters). Then, the number of true outcomes exceeds the number of possible outcomes- therefore the probability would seem to be more than one.

It is foolish, I agree, but it seems to make sense.

 

[epan]

Consider this- imagine the possibilities of what could be expressed on a single page of text. Such a page of text could possibly express:

• an infinitely true and perfectly expressed and summarised formulation of the meaning of life;
• a true and clear explanation of Trinity, the problem of evil, etc.
• the true biography of everyone who ever lived,
• the best poem every written,
• the secret name of God (if you believe in that kind of thing)
• a description of the scientific principle for a time machine, or cold fusion generator, a cure for cancer, or any number of things not yet invented.

Now, given the finitude of letters and other standard characters (puncutation marks, digits, etc.) it is obvious that the number of combinations making a single typed page is also finite. Maybe some mathematically minded person could work it out, as to hoe many combinations there could be.

So, this is my proposed experiment- set up a computer to type at random letters, characters, punction and spaces. This will produce a finite number of typed sheets. Read through each typed sheet to find the sheet which contains every conceivable truth.

Would it work?

 

[epan]

Consider this- imagine the possibilities of what could be expressed on a single page of text. Such a page of text could possibly express:

• an infinitely true and perfectly expressed and summarised formulation of the meaning of life;
• a true and clear explanation of Trinity, the problem of evil, etc.
• the true biography of everyone who ever lived,
• the best poem every written,
• the secret name of God (if you believe in that kind of thing)
• a description of the scientific principle for a time machine, or cold fusion generator, a cure for cancer, or any number of things not yet invented.

Now, given the finitude of letters and other standard characters (puncutation marks, digits, etc.) it is obvious that the number of combinations making a single typed page is also finite. Maybe some mathematically minded person could work it out, as to hoe many combinations there could be.

So, this is my proposed experiment- set up a computer to type at random letters, characters, punction and spaces. This will produce a finite number of typed sheets. Read through each typed sheet to find the sheet which contains every conceivable truth.

Would it work?

Well, if there are 238 characters in the ASCII character set (127 + extended), and an average of 2,000 characters on a page, then the number of possible permutations is: 2,000^238.

That is a large number.

 

[Alberti_Devoveo]

I realise traditionally proability is between 0 and 1, expressed as a fraction of the outcome in question over the possible outcomes.

Not traditionally, by definition. It is not something that can be loosened.

But, what if the number of possibilities of the outcome in question is infinite (e.g. there are an infinite number of possible true statements- since a truth could be stated about every possible aspect of, say, God), but the number of possible outcomes is limited (owing the the finite combinations of letters). Then, the number of true outcomes exceeds the number of possible outcomes- therefore the probability would seem to be more than one.

You cannot have it both ways: either the number of possibilities is infinite or it is finite. In either case, the probability of any one case is still 1 / total possibilities.

It also does not make sense whatsoever to say that the number of actual outcomes is unlimited while the number of possible outcomes is limited. The number of possible outcomes must, by definition, be equal to or greater than the number of actual outcomes.

It is foolish, I agree, but it seems to make sense.

Like I said before, you have no idea what you are talking about when it comes to probabilities, so of course it makes sense.

 

[Qoeleth]

Not traditionally, by definition. It is not something that can be loosened.

You cannot have it both ways: either the number of possibilities is infinite or it is finite. In either case, the probability of any one case is still 1 / total possibilities.

It also does not make sense whatsoever to say that the number of actual outcomes is unlimited while the number of possible outcomes is limited. The number of possible outcomes must, by definition, be equal to or greater than the number of actual outcomes.

Like I said before, you have no idea what you are talking about when it comes to probabilities, so of course it makes sense.

Let’s say there are an infinite number of possible truths, and X (a non-infinite number) possible sentences. Thus the proability is:
Infinity/X ( where X is less than infinity)

The answer of this calculation would seem to be more than one. Therefore, it is more than certain.

 

[rossum]

So, this is my proposed experiment- set up a computer to type at random letters, characters, punction and spaces. This will produce a finite number of typed sheets. Read through each typed sheet to find the sheet which contains every conceivable truth.

Would it work?

It has already been described by Jorge Luis Borges: The Library of Babel

rossum

 

[Alberti_Devoveo]

Let’s say there are an infinite number of possible truths, and X (a non-infinite number) possible sentences. Thus the proability is:
Infinity/X ( where X is less than infinity)

The answer of this calculation would seem to be more than one. Therefore, it is more than certain.

That does not make sense. An infinite number of truths could not be described by a finite number of sentences. If you have an infinite number of truths, then by necessity you would require an infinite number of sentences to write down those truths.

The answer to that calculation would certainly be more than one, but your calculation is inherently flawed from a physical and mathematical standpoint.

 

[Alberti_Devoveo]

Qoeleth: after some contemplation, you have not been describing a probability at all. You have been describing the ratio of truths to possible sentences. A probability is the chance that some event A occurs out of possible events A, B, C…, hence it written as probability = event A / total events. A ratio is just the quantitative relationship between two variables: ratio = X / Y.

Surely this ratio could be large, possibly infinite (if you accept an infinitude of truths), but is it relevant? Yes, but not as a probability. It is relevant in that it would take a very long time to run a program that spits out every possible permutation of the 80-or-so characters and a minimally as long time to process the pages (meaning it would take, at a minimum, the same amount of time to read in the data as it would to create it). But this tidbit of information has been given to you already, most recently by epan.

 

[epan]

That does not make sense. An infinite number of truths could not be described by a finite number of sentences. If you have an infinite number of truths, then by necessity you would require an infinite number of sentences to write down those truths.

The answer to that calculation would certainly be more than one, but your calculation is inherently flawed from a physical and mathematical standpoint.

For any set in which the sentences are of finite length, with a finite character set, then there is a finite number of sentences.

 

[Alberti_Devoveo]

For any set in which the sentences are of finite length, with a finite character set, then there is a finite number of sentences.

Then it follows that there cannot be an infinite number of truths because the set of truths must be contained within the set of sentences.

 

[Qoeleth]

Qoeleth: after some contemplation, you have not been describing a probability at all. You have been describing the ratio of truths to possible sentences. A probability is the chance that some event A occurs out of possible events A, B, C…, hence it written as probability = event A / total events. A ratio is just the quantitative relationship between two variables: ratio = X / Y.

Surely this ratio could be large, possibly infinite (if you accept an infinitude of truths), but is it relevant? Yes, but not as a probability. It is relevant in that it would take a very long time to run a program that spits out every possible permutation of the 80-or-so characters and a minimally as long time to process the pages (meaning it would take, at a minimum, the same amount of time to read in the data as it would to create it). But this tidbit of information has been given to you already, most recently by epan.

Well spotted. Now, the reason I hold there to be any infinite number of truths is this- imagine any possible moment, particle, action, point of view, etc. Now, these are surely infinite. And, in order to describe truly each of these, at least one (in fact more), truths could be generated. Ergo, there is an infinite number of truths.

But the fact that the number of true sentences must be finite (since the number of finite sentences itself, as has been shown, is finite), means that the number of truths exceed the number of possible expressions of truth. This would seem to be a paradox, because can there be a truth apart from the expression of truth? Or is it that one expression may contain more than one truth? Or are there some wholly inexpressible truths?

But if the classical ‘correspondence’ theory of truth is adopted, there can be no truth apart from the expression of truth.

 

[GEddie]

It has already been described by Jorge Luis Borges: The Library of Babel

rossum

And then further developed by the same author in “The Book of Sand.”

TBOB involves researchers in an infinite library uniformly stacked with books. The chance of them finding information they can use in this system, where by far most of the writings will be gibberish, is vanishingly small.

BOS reduces the Babel library to a single book having an infinite number of infinitely thin pages. In such a book, one could never find their place again, as each “page” would unfold into more than one; and although he could hold the thing in his hands, the book’s purchaser was likewise unable to find anything useful or helpful in it.

ICXC NIKA

 

[Alberti_Devoveo]

Well spotted. Now, the reason I hold there to be any infinite number of truths is this- imagine any possible moment, particle, action, point of view, etc. Now, these are surely infinite. And, in order to describe truly each of these, at least one (in fact more), truths could be generated. Ergo, there is an infinite number of truths.

As I pointed out in post #6, the number of particles in the universe is limited to about 10[sup]80[/sup], far less than the 10[sup]240[/sup] possible combinations of letters, symbols, and numbers on a keyboard (and which also ignores the separation of upper- and lower-cases).
Further, as I set out in post #49, the set of truths must be contained within the set of possible sentence. Why? Because the truths must be describable by some set of organized words. Since the set of sentences is clearly limited, the set of truths must also be limited.

Ergo, there is a finite number of truths.

But the fact that the number of true sentences must be finite (since the number of finite sentences itself, as has been shown, is finite), means that the number of truths exceed the number of possible expressions of truth. This would seem to be a paradox, because can there be a truth apart from the expression of truth? Or is it that one expression may contain more than one truth? Or are there some wholly inexpressible truths?

There is no paradox. The set of truths is limited by the set of sentences. I would discount the possibility of inexpressible truths, as truths must be explainable.

But if the classical ‘correspondence’ theory of truth is adopted, there can be no truth apart from the expression of truth.

Agreed.

 

[epan]

As I pointed out in post #6, the number of particles in the universe is limited to about 10[sup]80[/sup], far less than the 10[sup]240[/sup] possible combinations of letters, symbols, and numbers on a keyboard (and which also ignores the separation of upper- and lower-cases).
Further, as I set out in post #49, the set of truths must be contained within the set of possible sentence. Why? Because the truths must be describable by some set of organized words. Since the set of sentences is clearly limited, the set of truths must also be limited.

Ergo, there is a finite number of truths.

There is no paradox. The set of truths is limited by the set of sentences. I would discount the possibility of inexpressible truths, as truths must be explainable.

Agreed.

Further, though very large indeed, the number of states the number of particles in the universe may assume is finite. Any truth must be contained and expressed within the large finite system. Therefore the number of truths is finite.

Further, it a truth must be explainable, there are a finite number of people, each with a finite brain capacity, and therefore capable of perceiving a finite number of truths. This is true for the case of, any point in time=t, and for t+1 for all values of t. Therefore the number of truths is finite.

 

[Qoeleth]

As I pointed out in post #6, the number of particles in the universe is limited to about 10[sup]80[/sup], far less than the 10[sup]240[/sup] possible combinations of letters, symbols, and numbers on a keyboard (and which also ignores the separation of upper- and lower-cases).
Further, as I set out in post #49, the set of truths must be contained within the set of possible sentence. Why? Because the truths must be describable by some set of organized words. Since the set of sentences is clearly limited, the set of truths must also be limited.

Ergo, there is a finite number of truths.

But, how can the number of truths be finite, given that many truths could be expressed about each particle or moment, or sentence? Even if these were finite (and I don’t see how the number of moments could be finite?), truths could be then expressed about possible and actual other truths. Then truths could be expressed about those expressions of truth, and then about those truths, and so on, infinitely.

Let me demonstrate:
Today is Tuesday.
The first statement expressed that today is Tuesday.
The second statement identified that the preceding statement expressed that today is Tuesday.

And there are obviously an infinite number of mathematical truths:
2 x 1= 2, 2 x 2= 4, 2x 3= 6, etc. ad infinitum

Thus the number of truths would seem to be infinite.

 

[Alberti_Devoveo]

But, how can the number of truths be finite, given that many truths could be expressed about each particle or moment, or sentence?

Since there are only 10[sup]80[/sup] particles in the universe. Suppose that each of these particles possess 10[sup]80[/sup] truths to it. 10[sup]80[/sup] raised to 10[sup]80[/sup] truths in the universe. Last I checked, this number, though extremely large, is definitely not infinite.

I think the easiest explanation is that it takes words to explain, or express, a truth. Since we have a limited set of characters (roughly 86, I believe), we are limited to forming words of varying length of 1[sup]86[/sup] through, say, 45[sup]86[/sup] (debatable about the length of the longest word, but we do not need to be trivial). This is still a finite set of words. Each of these words must be contained, through syntactic definitions, within a sentence of varying length. Even if we assumed a sentence of 80 words, you still have a very finite number of sentences, words, and thus, truths.

Even if these were finite (and I don’t see how the number of moments could be finite?),

Since we know the big bang occurred roughly 13.7 billion years ago, I do not see how anyone could possibly think that time is infinite to this point.

truths could be then expressed about possible and actual other truths. Then truths could be expressed about those expressions of truth, and then about those truths, and so on, infinitely.

Let me demonstrate:
Today is Tuesday.
The first statement expressed that today is Tuesday.
The second statement identified that the preceding statement expressed that today is Tuesday.

And there are obviously an infinite number of mathematical truths:
2 x 1= 2, 2 x 2= 4, 2x 3= 6, etc. ad infinitum

Thus the number of truths would seem to be infinite.

Your first experiment fails because once it is not Tuesday, the first line is false (i.e., not a truth). Since you are confined to a single day of the week, and that day is finite, then the truth table you are building is finite.

The second experiment fails because it is a mathematical infinity, not a physical infinity (which is another topic in itself). Physical infinities do not exist, only potential infinities.

 

[Qoeleth]

Since there are only 10[sup]80[/sup] particles in the universe. Suppose that each of these particles possess 10[sup]80[/sup] truths to it. 10[sup]80[/sup] raised to 10[sup]80[/sup] truths in the universe. Last I checked, this number, though extremely large, is definitely not infinite.

I think the easiest explanation is that it takes words to explain, or express, a truth. Since we have a limited set of characters (roughly 86, I believe), we are limited to forming words of varying length of 1[sup]86[/sup] through, say, 45[sup]86[/sup] (debatable about the length of the longest word, but we do not need to be trivial). This is still a finite set of words. Each of these words must be contained, through syntactic definitions, within a sentence of varying length. Even if we assumed a sentence of 80 words, you still have a very finite number of sentences, words, and thus, truths.

Since we know the big bang occurred roughly 13.7 billion years ago, I do not see how anyone could possibly think that time is infinite to this point.

Your first experiment fails because once it is not Tuesday, the first line is false (i.e., not a truth). Since you are confined to a single day of the week, and that day is finite, then the truth table you are building is finite.

The second experiment fails because it is a mathematical infinity, not a physical infinity (which is another topic in itself). Physical infinities do not exist, only potential infinities.

Regarding the mathematical example- the truths which describe a mathematical infinity (which, granted, is only a potential infinity) would still seem to be an infinity of actual truths, since they are still actual truths about numbers, whether the number themselves are instantiated, or even conceived.

 

[Alberti_Devoveo]

Regarding the mathematical example- the truths which describe a mathematical infinity (which, granted, is only a potential infinity) would still seem to be an infinity of actual truths, since they are still actual truths about numbers, whether the number themselves are instantiated, or even conceived.

It would be a potential infinity of actual truths, but not an actual infinity about potential truths. Since it is merely a potential infinity, then one cannot obtain it in actuality.

 

[Qoeleth]

It would be a potential infinity of actual truths, but not an actual infinity about potential truths. Since it is merely a potential infinity, then one cannot obtain it in actuality.

Even if there are a potential infinity of actual truths (i.e. an infinitude of truths which COULD be expressed), and a finite number of possible expressions (combinations of letters and numbers), it would seem to follow that each of the expressions is true.